Do Dark Matter and Dark Energy Exist?

Numerous searches for the particle or particles responsible for dark matter have so far come up empty. What if dark matter doesn’t really exist? Could there be alternative explanation for the phenomena attributed to dark matter?

In the November 10, 2017 issue of the Astrophysical Journal, Swiss astronomer André Maeder presents an intriguing hypothesis that non-baryonic dark matter need not exist, nor dark energy either. In “Dynamical Effects of the Scale Invariance of the Empty Space: The Fall of Dark Matter?” he suggests that scale invariance of empty space (i.e. very low density) over time could be causing the phenomena we attribute to dark matter and dark energy.

What is scale invariance? In the cosmological context, it means that empty space and its properties do not change following an expansion or contraction. Scales of length, time, mass, energy, and so on are defined by the presence of matter. In the presence of matter, space is not scale invariant. But take the matter away, and empty space may have some non-intuitive properties. The expanding universe may require adding a small acceleration term that opposes the force of gravity. In the earlier denser universe, this acceleration term was tiny in comparison to the rate at which the expansion was slowing down, but in the later emptier universe, the acceleration term dominates. Sound like dark energy, doesn’t it? But maybe it is an inherent property of empty space itself.

The existence of dark matter is primarily suggested by two observed dynamical anomalies:

Many spiral galaxies have a well-known property that beyond a certain distance from their centers, their rotation rate (the orbital velocity of stars at that distance) stays nearly constant rather than decreasing as one would expect from Keplerian motion / Newtonian dynamics (think planets orbiting the Sun in our own solar system— the farther the planet is from the Sun, the slower it orbits). Only there seems to be evidence that the rotation curves of galaxies when they are young (as seen in the high-redshift universe) do have a Keplerian gradient, but in the present-day universe the rotation curve is flat. So, it appears, flat rotation curves could be an age effect. In other words, in the outer regions of spiral galaxies, stars may be orbiting at the same velocity as they did in the past when they were closer to the galactic center. Maeder writes:

…the relatively flat rotation curves of spiral galaxies is an age effect from the mechanical laws, which account for the scale invariant properties of the empty space at large scales. These laws predict that the circular velocities remain the same, while a very low expansion rate not far from the Hubble rate progressively extends the outer layers, increasing the radius of the Galaxy and decreasing its surface density like 1/t.

We need to study the rotation curves (as a function of galactocentric radius all the way out to the outermost reaches of the galaxy) of many more galaxies at different redshifts (and thus ages) to help us test the validity of the scale invariant vs. dark matter hypotheses. Maeder suggests a thorough rotation study of two massive and fast-rotating galaxies, UGC 2953 (a.k.a. IC 356; 50-68 Mly) and UGC 2487 (a.k.a. NGC 1167; 219-225 Mly), would be quite interesting.

The observed motions of galaxies within many galaxy clusters seems to indicate there is a substantial amount of unseen mass within these clusters, through application of the virial theorem. However, the motions within some galaxy clusters such as Coma (336 Mly) and Abell 2029 (1.1 Gly) may be explainable without the need to resort to “exotic” dark matter.

Then there’s the AVR (Age-Velocity Dispersion Relation) problem which, incidentally, has nothing to do with dark matter. But it may offer evidence for the scale invariant hypothesis. It is convenient to specify the motion of a star in a spiral galaxy such as the Milky Way in a galactocentric coordinate system.

U = component of velocity towards the galaxy center

V = component of velocity in the direction of galactic rotation

W = component of velocity orthogonal to the galactic plane

Maeder writes:

The AVR problem is that of explaining why the velocity dispersion, in particular for the W-component, considerably increases with the age of the stars considered … Continuous processes, such as spiral waves, collisions with giant molecular clouds, etc… are active in the disk plane and may effectively influence the stellar velocity distributions. However…vertical heating (the increase of the dispersion σW) is unexpected, since the stars spend most of their lifetime out of the galactic plane.